title: Eigen decomposition solution to the one-dimensional time-dependent photon transport equation.
abstract: The time-dependent one-dimensional photon transport (radiative transfer) equation is widely used to model light propagation through turbid media with a slab geometry, in a vast number of disciplines. Several numerical and semi-analytical techniques are available to accurately solve this equation. In this work we propose a novel efficient solution technique based on eigen decomposition of the vectorized version of the photon transport equation. Using clever transformations, the four variable integro-differential equation is reduced to a set of first order ordinary differential equations using a combination of a spectral method and the discrete ordinates method. An eigen decomposition approach is then utilized to obtain the closed-form solution of this reduced set of ordinary differential equations.
authors.affiliation: School of Engineering, Faculty of Science and Technology, Deakin University, Geelong, Victoria 3217, Australia. chintha.handapangoda@deakin.edu.au
authors.forename: Chintha C
authors.initials: CC
authors.lastname: Handapangoda
authors.forename: Pubudu N
authors.initials: PN
authors.lastname: Pathirana
authors.forename: Malin
authors.initials: M
authors.lastname: Premaratne